A Local-time Correspondence for Stochastic Partial Differential Equations

  title={A Local-time Correspondence for Stochastic Partial Differential Equations},
  author={Davar Khoshnevisan and EULALIA NUALART},
It is frequently the case that a white-noise-driven parabolic and/or hyperbolic stochastic partial differential equation (SPDE) can have random-field solutions only in spatial dimension one. Here we show that in many cases, where the “spatial operator” is the L-generator of a Lévy process X, a linear SPDE has a random-field solution if and only if the symmetrization of X possesses local times. This result gives a probabilistic reason for the lack of existence of random-field solutions in… CONTINUE READING

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